A spatiotemporal model of meningococcal meningitis with direct and indirect transmission.

We extend an ordinary differential equation (ODE) model for the meningococcal meningitis disease to a partial differential equation (PDE). This extension istwofold: (i) consideration of two modes of contamination, namely through a direct transmission (human to human) and an indirect transmission (via free‐living bacteria). (ii) consideration of the human movement and the dispersal of bacteria in a heterogeneous environment. Furthermore we show the existence of the solutions and define the basic reproduction number R0 for the model. Additionally, the existence and the stability of both disease‐free and endemic equilibria were investigated. The sensitivity of R0 and the endemic state with respect of the model parameters were studied. Numerical computations of the spreading bacteria are carried out to illustrate our mathematical results. [ABSTRACT FROM AUTHOR]